Because their main source of revenue now is from filing fees:
Federal courthouses would remain open under the terms of the Anti-Deficiency Act, the federal law that calls for “essential” work to continue in the event that federal funding is frozen. Most judicial services are considered essential; judges would keep working, legal filings would still be processed and federal defenders would continue to be assigned to indigent defendants.
For the first two weeks, the courts would use revenue from filing fees and long-term appropriations that are not part of the annual budget to pay its staffers as normal, according to a memorandum from the Administrative Office of the U.S. Courts sent last week. Courts were encouraged to conserve as much as possible by deferring non-crucial expenses.